STUDENT SOLUTION MANUAL
CHAPTER 2
Section 2-2
2-43
3 digits between 0 and 9, so the probability of any three numbers is 1/(10*10*10);
3 letters A to Z, so the probability of any three numbers is 1/(26
Stat 330 - Tutorial 9 Solution
Brief solutions are available below.
1.
(a) We can write
l() = log(C )
1
2 2
n
(xi )2
i=1
where C is some constant, not in terms of . Therefore, the estimator is = X .
Stat 330 - Tutorial 5 Solution
1.
E [(Y h(X )2 ] = E
Y g (X ) + g (X ) h(X )
=E
Y g (X )
2
=E
Y g (X )
2
2
+ 2 Y g (X ) g (X ) h(X ) + g (X ) h(X )
+ 2E
Y g (X ) g (X ) h(X )
+E
2
g (X ) h(X )
0 (expe
Stat 330 - Tutorial 7 Solution
1.
t 1)
Y | = P oi() = E (Y | = ) = , V ar(Y | = ) = , MY |= (t) = e(e
= E (Y |) = , V ar(Y |) = , MY | (t) = e(e
t 1)
Gamma(, ) = E () = , V ar() = 2 , M (t) = (1 t)
T
Stat 330 - Tutorial 9
iid
1. Suppose X1 , . . . , Xn N (, 2 ) where is known. Suppose we would like to test H0 :
= 0 vs HA : = 0 .
(a) Construct the LR test statistic under H0 .
(b) Show that the 2 d
Stat 330 - Tutorial 7
1. (Question 28 from the back of the course notes) Assume that Y denotes the number
of bacteria in a cubic centimetre of liquid and that Y | = P OI (). Further assume that varies
Stat 330 - Tutorial 5
1. (Minimum Mean Squared Error) Let h(X ) be any function of X and g (X ) = E (Y |X ).
Show that the g (X ) minimizes the mean squared error, that is,
E [(Y g (X )2 ] E [(Y h(X )
University of Waterloo
STAT 330 Term Test #2
Term: Spring
Year:
2012
Student Name (Print):
UW Student ID Number:
UW Student Userid:
Instructor (Circle one):
1. Javid Ali
2. Pengfei Li
Course Abbreviat
Stat 330 - Tutorial 3
Exercise 3.3.6 (Page 34 of supplementary notes). Suppose X and Y are continuous random
variables with joint p.d.f.
f (x, y ) =
k
, 0 < x < , 0 < y <
(1 + x + y )3
and 0 otherwis
Tutorial 3 Solution
We are given
f (x, y ) =
k
, 0 < x < , 0 < y <
(1 + x + y )3
and 0 otherwise.
The integral over the entire rst quadrant (the support of (X, Y ) should be equal to 1. That is,
0
0
Stat 330 - Tutorial 4
1. (SOA Exam P Past Question) An insurance company sells two types of auto insurance
policies: Basic and Deluxe. The time until the next Basic Policy claim is an exponential
rand
ChE 622 Winter 2008 Assignment #2
Due Date: Monday, February 11, 2008 at 3:00 pm
1. The following ( X X ) 1 , X y and residual sum of squares were obtained from the
regression of plant dry weight in g
ChE 622 Fall 2009 Assignment #2
Due Date: Thursday, October 15, 2009 at 4:00 pm
1. A study was performed on the wear of a bearing y and its relationship to x1 = oil
viscosity and x2 = load. The follow
qaChE 622 Winter 2007 Assignment #2
Due Date: Monday, February 5, 2007 at noon.
1.
The cloud point of a liquid is a measure of the degree of crystallization in a stock
that can be measured by a refrac
ChE 622 Assignment #1
January 7, 2011
Due Date: Tuesday, January 18, 2011 by 4 pm.
1.
Two catalysts are being analyzed to determine how they affect the mean yield of a chemical
process. Specifically,
ChE 325/622 Solutions to Assignment #1 Winter 2010
1.
Inspection of the data reveals that one observation (82.1) is very much larger than
the other brightness measurements. (In fact this is a real dat
ChE 622 Solutions to Assignment #1 F2009
1.
Given: n=20,
s=16g
Hypotheses: H0 : H1: 510
-2.795
Assume a 5% significance level Zcrit=Z0.025=-1.96
We reject the hypothesis that =510g.Therefore, we canno
ChE 622 Assignment #1
solutions
1.) Catalyst 1:
x1 92.255
s1 2.385
(7 d.f.)
s12 5.698
Catalyst 2
(7 d.f.)
x 2 92.7325
s 2 2.9385
s 22 8.6348
too few observations to check equality of variances : use e
ChE 622 Solutions to Assignment #1 Winter 2008
Inspection of the data reveals that one observation (82.1) is very much larger than
the other brightness measurements. (In fact this is a real data set t
Stat 330 - Tutorial 2
1. Suppose X BIN (n, p).
(a) Find E (X (k) ) and use the result to nd E (X ) and V ar(X ).
(b) Find the mgf of X and use the mgf to nd E (X ) and V ar(X ).
2. 3.2.5 (Page 31 of s
Stat 330 - Tutorial 1
1.
( x ) 2
1
.
(a) X N (, 2 ) = f (x; ) = exp
2 2
2
1
x2
Note that f0 (x) = f (x; = 0) = exp 2 .
2
2
Since f0 (x ) = f (x; ), by denition, is a location parameter.
1
x2
(b) If
Stat 330 - Tutorial 1
1. Suppose X N (, 2 ).
(a) Show that is a location parameter.
(b) Show that if = 0, then is a scale parameter.
2. If U is uniformly distributed on (0, 1), nd the probability dens
STAT 330
Mathematical Statistics
Assignment 1
Due: Thursday, May 31, 2012
1. Suppose X follows Geo(p) distribution with 0 < p < 1. That is,
f (x) = (1 p)x p, x = 0, 1, . . .
with 0 < p < 1.
(a) Find t
STAT 330 F13 Term Test II Information
Time and Date: Friday, Nov. 22, 3:30 4:20.
Location: Same as for Term Test I:
Section 001 (Y. Ning):
A P (Last Name): MC 2017
QZ
: MC 2054
Section 002 (P. Balka):
STAT 330 F13 Term Test I Information
Time and Date: Friday, Oct.18. 3:30 4:20.
Location:
Section 001 (Y. Ning):
A P (Last Name): MC 2017
QZ
: MC 2054
Section 002 (P. Balka):
DC 1350
Format:
Closed boo
Assignment #1 (Due Oct 10th)
Note: Please submit the assignment to Drop Box 15, slot 2 (Y. Ning) and slot 4
(P. Balka) outside MC 4006/4007. The assignment will be collected at 5:00pm.
Late submission
STAT 330 F13 Final Exam Information
Time and Location: See official exam schedule.
Format:
Same format and style as term tests.
Exam aides: None. NO CALCULATORS. Relevant distributions (e.g. chi-squar
STAT 330 - Assignment #4
Due Monday, Dec. 2 at 5:00 pm in Drop Box 15 (slot 2 (Y. Ning) and slot 4 (P. Balka) outside MC
4006/4007.
1) Let X i ~ U ( 0 ,1), i 1, 2 ,., n independen tly
a) Find the limi